Question

If the sum of two natural numbers is $27$ and their product is $182$, find the numbers.

Answer 1

Let one number be $x$ and another natural number $27-x$

$\begin{array}{c}x\left(27-x\right)=2\\ 27x-x^2=182\\ 27x-x^2-182=0\\ -x^2+27x-182=0\\ x^2-27x+182=0\\ x^2-14x-13x+182=0\\ x\left(x-14\right)-13\left(x-14\right)=0\\ \left(x-14\right)\left(x-13\right)\\ x=14\\ x=13\end{array}$